"The FBI is not 100 percent focused on this one guy," the source said. "Agents are not just guided by what he claims."

Before Snowden stepped from the shadows to claim he was the source of a series of headline-grabbing reports in the U.K.'s The Guardian newspaper and in The Washington Post, the columnist who broke the stories for The Guardian, Glenn Greenwald, told ABC News' "This Week" that he was "not going to confirm there is only one individual - there could be more than one."

Since Snowden's public confession late Sunday, neither Greenwald nor the other reporters involved in the stories have mentioned a second source, but investigators noted that in his confession, Snowden never explicitly stated which documents he handed over to the newspapers.

National security veterans said they're skeptical, for example, that Snowden, a private information technology contractor working for the NSA in Hawaii, could have had access to a Top Secret order from the super-secretive Foreign Intelligence Surveillance Act (FISA) court. That order, which compelled Verizon to hand over phone call information on millions of its customers to the government, was the basis of Greenwald's first report late last week.

"It makes no sense to me," a former U.S. counterintelligence official said. According to insiders, there has never been such a breach of the FISA court in all of its 35-year existence.

The law enforcement source also said that the FBI was on Snowden's trail as a possible leaker well before he revealed himself online, as first reported by The Daily Beast.

"There were indications he was involved before that," the source said.

According to The Guardian, which revealed Snowden's identity in a video and print interview, Snowden told his NSA supervisor three weeks ago that he had to be away from work for "a couple of weeks" to get treatment for epilepsy, which he said had revealed itself in seizures last year. He also told his girlfriend he would be away for a few weeks and gave no explanation.

"That is not an uncommon occurrence for someone who has spent the last decade working in the intelligence world," he told the paper.

On May 20, Snowden boarded a flight for Hong Kong and has been hiding out there ever since. He checked out of a swanky hotel there just today, an employee there told ABC News.

With top U.S. officials calling for his prosecution and others offering to protect him, Snowden remains on the run and, according to The Guardian, in possession of several more damning government files. The Justice Department is in the "initial stages of an investigation" into the recent unauthorized disclosures, a DOJ spokesperson told The Associated Press Sunday without naming Snowden.